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Séminaire Lotharingien de Combinatoire, B44c (2000), 3 pp.

# Herbert S. Wilf

#
Identically Distributed Pairs of Partition Statistics

**Abstract.**
We show that many theorems which assert that two kinds of partitions of the
same integer *n* are equinumerous are actually special cases of a much
stronger form of equality. We show that in fact there correspond partition
statistics *X* and *Y* that have identical distribution functions. The
method is an extension of the principle of sieve-equivalence, and it yields
simple criteria under which we can infer this identity of distribution
functions.

Received: April 25, 2000; Accepted: May 19, 2000.

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